According to mintzberg's typology, a manager who evaluates the performance of other managers in different tasks and takes corrective action to improve their performance is a

Monitor

Explanation:

Henry Mintzberg described a manager who evaluates the performance of other managers in different tasks and takes corrective action to improve their performance as a monitor.

Manager’s job is highly orchestrated in which managers rationally calculate the best way to use resources to achieve the organizational goals. Henry Mintzberg by following the manager around and observe what they actually do hour by hour and day by day. He transformed or identified ten set of responsibilities or kinds of specific roles, that capture the dynamic nature of managerial work.He has grouped these roles as  whether the responsibility is primarily, decisional, interpersonal or informational in nature.

As described under the role Informational the specific role of Monitor  who evaluate the performance of manager in different tasks and take corrective actions to improve their performance; watch for changes occurring in the external and internal environments that may affect the organization in the future